Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Algebra II Quiz: Lessons 7.1 through 7.4 Review

Graph:

1. f x( ) = 4x

Name: ________________________ ID: A

2

____ 2. Graph the function: f x( ) = 3x

Name: ________________________ ID: A

3

a.

b.

Name: ________________________ ID: A

4

c.

d.

____ 3. Find the y-intercept of the equation. y = − 3 ⋅ 7x

a. 4 b. –21 c. –3 d. 7

4. The amount of money, A, accrued at the end of n years when a certain amount, P, is invested at a compound

annual rate, r, is given by A = P(1 + r)n. If a person invests $250 in an account that pays 10% interest

compounded annually, find the balance after 15 years.

Name: ________________________ ID: A

5

____ 5. The amount of money, A, accrued at the end of n years when a certain amount, P, is invested at a compound

annual rate, r, is given by A =P 1+ r( )n. If a person invests $310 in an account that pays 8% interest

compounded annually, find the balance after 5 years.

a. $455 b. $2790 c. $13,950 d. $443

6. The projected worth (in millions of dollars) of a large company is modeled by the equation y = 256 1.04( )x.

The variable x represents the number of years since 1997. What is the projected annual percent of growth,

and what should the company be worth be in 2007?

____ 7. The projected worth (in millions of dollars) of a large company is modeled by the equation y = 241 1.04( )x.

The variable x represents the number of years since 1997. What is the projected annual percent of growth,

and what should the company be worth in 2001?

a. 14%; $293.21 million c. 14%; $250.64 million

b. 4%; $271.09 million d. 4%; $281.94 million

8. Find the value of $1000 deposited for 8 years in an account paying 8% annual interest compounded semiannually.

9. How much money must be deposited now in an account paying 7% annual interest, compounded yearly, to have a balance of $1000 after 6 years?

____ 10. Sara bought 6 fish. Every month the number of fish she has doubles. After m months she will have F fish,

where F = 6 ⋅2m. How many fish will Sara have after 2 months if she keeps all of them and the fish stay

healthy?

a. 20 b. 10 c. 144 d. 24

____ 11. If there are initially 4000 bacteria in a culture, and the number of bacteria double each hour, the number of

bacteria after t hours can be found using the formula N = 4000 2tÊËÁÁÁ

ˆ¯˜̃̃ . How many bacteria will be present after

9 hours?

a. 2,048,000 b. 4,096,000 c. 1,024,000 d. 72,000

Name: ________________________ ID: A

6

____ 12. Graph the function: f x( ) =1

4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

x

Name: ________________________ ID: A

7

a.

b.

Name: ________________________ ID: A

8

c.

d.

13. Describe y=2.9x as an example of exponential growth or exponential decay.

Name: ________________________ ID: A

9

Graph:

____ 14. f(x) = 21

4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

x

a. c.

b. d.

Writing:

15. How does changing the value of b affect the graph of an exponential equation of the form y = abx?

Simplify:

____ 16. 7e

19

35e6

a. 5e25

c. 5e13

b.1

5e

13d.

1

5e

25

Simplify the expression.

17. ex

⋅ 6e3x − 1

Name: ________________________ ID: A

10

____ 18. Graph f x( ) = − 3 + ex.

a. c.

b. d.

19. Is f x( ) = 13.7e−0.04t

an example of exponential growth or decay?

20. Sketch the graph of the function. f x( ) =1

3e

x− 2

____ 21. If $2500 is invested at a rate of 11% compounded continuously, find the balance in the account after 4 years.

Use the formula A =Pert

.a. $3795.18 b. $3881.77 c. $4333.13 d. $18472.64

____ 22. The formula A = 2000ert

can be used to find the dollar value of an investment of $2000 after t years when the

interest is compounded continuously at a rate of r percent. Find the value of the investment after 6 years if

the interest rate is 7%. Find the value of the investment after 12 years if the interest rate is 8%.

a. $3043.92; $2920.47 c. $3043.92; $5223.39

b. $4901.85; $5223.39 d. $4901.85; $2920.47

True or False:

23. The formula for interest compounded continuously is A = Pet.

24. The formula for interest compounded continuously is A = Pert.

Name: ________________________ ID: A

11

Evaluate:

____ 25. log3729

a.1

6b. 18 c. 6 d.

1

18

____ 26. Graph the function y = 1.2x and its reflection over the line y = x. Is the reflection the graph of a function?

a.

No

c.

No

b.

Yes

d.

Yes

Name: ________________________ ID: A

12

Graph:

____ 27. y = log3 x

a. c.

b. d.

____ 28. Use the formula R = log10 I , where R is the measurement of the Richter scale and I is the intensity, to find the

Richter scale measurement of an earthquake with intensity 53,000,000.

a. 7.7243 b. 1.77858 c. 0.77243 d. 17.7858

29. Evaluate ln e−4

.

Graph the function. State the domain and range.

30. y = ln x + 2( )

ID: A

1

Algebra II Quiz: Lessons 7.1 through 7.4 Review

Answer Section

1. ANS:

PTS: 1 DIF: Level B REF: MAL21000 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: function | graph | exponentBLM: Knowledge NOT: 978-0-618-65615-8

2. ANS: B PTS: 1 DIF: Level B REF: MAL21002

TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: function | graph | exponentialBLM: Knowledge NOT: 978-0-618-65615-8

3. ANS: C PTS: 1 DIF: Level B REF: MAL21004

TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: exponential | equationBLM: Knowledge NOT: 978-0-618-65615-8

4. ANS:

$1044

PTS: 1 DIF: Level B REF: MAL21006 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth FunctionsKEY: word | log | compound interest BLM: Application NOT: 978-0-618-65615-8

5. ANS: A PTS: 1 DIF: Level B REF: MAL21007

STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth FunctionsKEY: word | log | compound interest BLM: Application NOT: 978-0-618-65615-8

6. ANS:

4%; $378.94 million

PTS: 1 DIF: Level B REF: MAL21008 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: word | exponential growthBLM: Application NOT: 978-0-618-65615-8

7. ANS: D PTS: 1 DIF: Level B REF: MAL21009TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: word | exponential | growthBLM: Application NOT: 978-0-618-65615-8

ID: A

2

8. ANS:

$1872.98

PTS: 1 DIF: Level A REF: MAL21014 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth FunctionsKEY: compound interest BLM: Application NOT: 978-0-618-65615-8

9. ANS:

$666.34

PTS: 1 DIF: Level B REF: MAL21017 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth FunctionsKEY: compound interest BLM: Application NOT: 978-0-618-65615-8

10. ANS: D PTS: 1 DIF: Level B REF: MAL21020TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: law of exponents | wordBLM: Application NOT: 978-0-618-65615-8

11. ANS: A PTS: 1 DIF: Level B REF: MAL21022TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: word | exponential growthBLM: Application NOT: 978-0-618-65615-8

12. ANS: C PTS: 1 DIF: Level B REF: MAL21028TOP: Lesson 7.2 Graph Exponential Decay Functions KEY: graph | functionBLM: Knowledge NOT: 978-0-618-65615-8

13. ANS: exponential growth

PTS: 1 DIF: Level B REF: MAL21029 NAT: NCTM 9-12.ALG.1.cSTA: MI.MIGLC.MTH.06.9-12.A2.5.2 TOP: Lesson 7.2 Graph Exponential Decay FunctionsKEY: exponential growth | exponential decay BLM: ComprehensionNOT: 978-0-618-65615-8

14. ANS: D PTS: 1 DIF: Level B REF: MAL21031TOP: Lesson 7.2 Graph Exponential Decay Functions KEY: graph | exponential functionBLM: Knowledge NOT: 978-0-618-65615-8

15. ANS: Sample answer: For b > 0, as the value of b increases, the curve slopes upward faster; that is, the value of y increases at a faster rate. For 0 < b < 1, as the value of b increases, the curve slopes downward slower; that is, the value of y decreases at a slower rate.

PTS: 1 DIF: Level B REF: MAL21032 NAT: NCTM 9-12.ALG.1.cTOP: Lesson 7.2 Graph Exponential Decay Functions KEY: graph | exponentialBLM: Analysis NOT: 978-0-618-65615-8

16. ANS: B PTS: 1 DIF: Level B REF: MAL21041TOP: Lesson 7.3 Use Functions Involving e KEY: exponent | exponential | rules | simplify BLM: ComprehensionNOT: 978-0-618-65615-8

ID: A

3

17. ANS:

6e4x − 1

PTS: 1 DIF: Level B REF: MAL21042 TOP: Lesson 7.3 Use Functions Involving e KEY: exponent | multiply | eBLM: Comprehension NOT: 978-0-618-65615-8

18. ANS: D PTS: 1 DIF: Level B REF: MAL21049

TOP: Lesson 7.3 Use Functions Involving e KEY: function | graph | exponentialBLM: Knowledge NOT: 978-0-618-65615-8

19. ANS:

Decay

PTS: 1 DIF: Level A REF: MAL21052 STA: MI.MIGLC.MTH.06.9-12.A2.5.2TOP: Lesson 7.3 Use Functions Involving e KEY: function | exponential growth | exponential decay BLM: KnowledgeNOT: 978-0-618-65615-8

20. ANS:

PTS: 1 DIF: Level B REF: MAL21053 TOP: Lesson 7.3 Use Functions Involving e KEY: graph | exponential function | eBLM: Comprehension NOT: 978-0-618-65615-8

21. ANS: B PTS: 1 DIF: Level B REF: MAL21058

STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.3 Use Functions Involving eKEY: word | interest | compound | continuous BLM: ApplicationNOT: 978-0-618-65615-8

22. ANS: C PTS: 1 DIF: Level B REF: MAL21060STA: MI.MIGLC.MTH.06.9-12.L2.2.3 | MI.MIGLC.MTH.06.9-12.A1.2.9 | MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.3 Use Functions Involving eKEY: interest | continuous | compounded continuously BLM: ApplicationNOT: 978-0-618-65615-8

ID: A

4

23. ANS:

False

PTS: 1 DIF: Level B REF: MAL21062 TOP: Lesson 7.3 Use Functions Involving e KEY: word | interest | e | compounded continuously BLM: ComprehensionNOT: 978-0-618-65615-8

24. ANS:

True

PTS: 1 DIF: Level B REF: MAL21063 TOP: Lesson 7.3 Use Functions Involving e KEY: e | compounded continuously | word | interest BLM: ComprehensionNOT: 978-0-618-65615-8

25. ANS: C PTS: 1 DIF: Level A REF: MAL21066TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: log | evaluate | exponential BLM: Knowledge NOT: 978-0-618-65615-8

26. ANS: B PTS: 1 DIF: Level B REF: MAL21076NAT: NCTM 9-12.GEO.3.a TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: graph | exponential | inverse | function BLM: ComprehensionNOT: 978-0-618-65615-8

27. ANS: C PTS: 1 DIF: Level B REF: MAL21081NAT: NCTM 9-12.ALG.1.c TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: log | graph BLM: Comprehension NOT: 978-0-618-65615-8

28. ANS: A PTS: 1 DIF: Level B REF: MAL21110STA: MI.MIGLC.MTH.06.9-12.A1.2.7 TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: logarithms | word BLM: Application NOT: 978-0-618-65615-8

29. ANS: -4

PTS: 1 DIF: Level B REF: MAL21073 TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: logarithm | e BLM: Knowledge NOT: 978-0-618-65615-8

ID: A

5

30. ANS:

Domain: x > −2; Range: all real numbers

PTS: 1 DIF: Level B REF: MAL21089 NAT: NCTM 9-12.ALG.1.cSTA: MI.MIGLC.MTH.06.9-12.A2.5.2 TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic FunctionsKEY: log | graph BLM: Comprehension NOT: 978-0-618-65615-8